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rect{fill:var(--md-mermaid-edge-color)!important;stroke:none!important}.statediagram-cluster.statediagram-cluster .inner{fill:var(--md-default-bg-color)}.statediagram-cluster rect{fill:var(--md-mermaid-node-bg-color);stroke:var(--md-mermaid-node-fg-color)}.statediagram-state rect.divider{fill:var(--md-default-fg-color--lightest);stroke:var(--md-default-fg-color--lighter)}defs #statediagram-barbEnd{stroke:var(--md-mermaid-edge-color)}[id^=entity] path,[id^=entity] rect{fill:var(--md-default-bg-color)}.relationshipLine{stroke:var(--md-mermaid-edge-color)}defs .marker.oneOrMore.er *,defs .marker.onlyOne.er *,defs .marker.zeroOrMore.er *,defs .marker.zeroOrOne.er 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I,c=s.pipe(he(),ye(!0));re([s,Re(e),Et(e)]).pipe(Q(c),Xe(1,je)).subscribe({next([{active:l},u]){let p=wt(l),{width:d}=Ae(l);e.style.setProperty("--md-indicator-x",`${p.x}px`),e.style.setProperty("--md-indicator-width",`${d}px`);let m=ln(n);(p.xm.x+u.width)&&n.scrollTo({left:Math.max(0,p.x-16),behavior:"smooth"})},complete(){e.style.removeProperty("--md-indicator-x"),e.style.removeProperty("--md-indicator-width")}}),re([Ut(n),Re(n)]).pipe(Q(c)).subscribe(([l,u])=>{let p=Mr(n);i.hidden=l.x<16,a.hidden=l.x>p.width-u.width-16}),R(b(i,"click").pipe(f(()=>-1)),b(a,"click").pipe(f(()=>1))).pipe(Q(c)).subscribe(l=>{let{width:u}=Ae(n);n.scrollBy({left:u*l,behavior:"smooth"})}),r.pipe(Q(c),L(l=>o.includes(l))).subscribe(l=>l.click()),n.classList.add("tabbed-labels--linked");for(let l of o){let 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fc({document$:e,tablet$:t}){e.pipe(g(()=>P(".md-toggle--indeterminate")),$(r=>{r.indeterminate=!0,r.checked=!1}),oe(r=>b(r,"change").pipe(Xn(()=>r.classList.contains("md-toggle--indeterminate")),f(()=>r))),pe(t)).subscribe(([r,n])=>{r.classList.remove("md-toggle--indeterminate"),n&&(r.checked=!1)})}function Hp(){return/(iPad|iPhone|iPod)/.test(navigator.userAgent)}function mc({document$:e}){e.pipe(g(()=>P("[data-md-scrollfix]")),$(t=>t.removeAttribute("data-md-scrollfix")),L(Hp),oe(t=>b(t,"touchstart").pipe(f(()=>t)))).subscribe(t=>{let r=t.scrollTop;r===0?t.scrollTop=1:r+t.offsetHeight===t.scrollHeight&&(t.scrollTop=r-1)})}Object.entries||(Object.entries=function(e){let t=[];for(let r of Object.keys(e))t.push([r,e[r]]);return t});Object.values||(Object.values=function(e){let t=[];for(let r of Object.keys(e))t.push(e[r]);return t});typeof Element!="undefined"&&(Element.prototype.scrollTo||(Element.prototype.scrollTo=function(e,t){typeof e=="object"?(this.scrollLeft=e.left,this.scrollTop=e.top):(this.scrollLeft=e,this.scrollTop=t)}),Element.prototype.replaceWith||(Element.prototype.replaceWith=function(...e){let t=this.parentNode;if(t){e.length===0&&t.removeChild(this);for(let r=e.length-1;r>=0;r--){let n=e[r];typeof n=="string"?n=document.createTextNode(n):n.parentNode&&n.parentNode.removeChild(n),r?t.insertBefore(this.previousSibling,n):t.replaceChild(n,this)}}}));function $p(){return location.protocol==="file:"?ar(`${new URL("search.js",Mn.base)}`).pipe(f(()=>__index),_e(()=>Ke),se(1)):et(new URL("search.json",Mn.base))}document.documentElement.classList.remove("no-js");document.documentElement.classList.add("js");var vt=Si(),Ur=Za(),hr=ts(Ur),hc=Xa(),ze=cs(),$o=Ir("(min-width: 60em)"),vc=Ir("(min-width: 76.25em)"),bc=rs(),Mn=Ue(),gc=Le(".md-search")?$p():Ke,Po=new I;oc({alert$:Po});nc({document$:vt});var Io=new 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b/en/chapter_computational_complexity/summary/index.html index 13d1c55f8..6791efe7f 100644 --- a/en/chapter_computational_complexity/summary/index.html +++ b/en/chapter_computational_complexity/summary/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_computational_complexity/time_complexity/index.html b/en/chapter_computational_complexity/time_complexity/index.html index a2705fc28..ef8f85852 100644 --- a/en/chapter_computational_complexity/time_complexity/index.html +++ b/en/chapter_computational_complexity/time_complexity/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_data_structure/basic_data_types/index.html b/en/chapter_data_structure/basic_data_types/index.html index 99d5ce885..5a7fce88a 100644 --- a/en/chapter_data_structure/basic_data_types/index.html +++ b/en/chapter_data_structure/basic_data_types/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_data_structure/character_encoding/index.html b/en/chapter_data_structure/character_encoding/index.html index c37dd0253..3acf592bb 100644 --- a/en/chapter_data_structure/character_encoding/index.html +++ b/en/chapter_data_structure/character_encoding/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_data_structure/classification_of_data_structure/index.html b/en/chapter_data_structure/classification_of_data_structure/index.html index 3da147c55..ebc5b453b 100644 --- a/en/chapter_data_structure/classification_of_data_structure/index.html +++ b/en/chapter_data_structure/classification_of_data_structure/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_data_structure/index.html b/en/chapter_data_structure/index.html index 81d08a627..d46491396 100644 --- a/en/chapter_data_structure/index.html +++ b/en/chapter_data_structure/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_data_structure/number_encoding/index.html b/en/chapter_data_structure/number_encoding/index.html index 7824b9a18..7692a5c39 100644 --- a/en/chapter_data_structure/number_encoding/index.html +++ b/en/chapter_data_structure/number_encoding/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_data_structure/summary/index.html b/en/chapter_data_structure/summary/index.html index 0fcdc7a73..be1a53ce0 100644 --- a/en/chapter_data_structure/summary/index.html +++ b/en/chapter_data_structure/summary/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_divide_and_conquer/binary_search_recur/index.html b/en/chapter_divide_and_conquer/binary_search_recur/index.html index 2027a8c46..3c68d57be 100644 --- a/en/chapter_divide_and_conquer/binary_search_recur/index.html +++ b/en/chapter_divide_and_conquer/binary_search_recur/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_divide_and_conquer/build_binary_tree_problem/index.html b/en/chapter_divide_and_conquer/build_binary_tree_problem/index.html index f4659f3fc..cd25d44b7 100644 --- a/en/chapter_divide_and_conquer/build_binary_tree_problem/index.html +++ b/en/chapter_divide_and_conquer/build_binary_tree_problem/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_divide_and_conquer/divide_and_conquer/index.html b/en/chapter_divide_and_conquer/divide_and_conquer/index.html index e0bac8264..aa3a68919 100644 --- a/en/chapter_divide_and_conquer/divide_and_conquer/index.html +++ b/en/chapter_divide_and_conquer/divide_and_conquer/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_divide_and_conquer/hanota_problem/index.html b/en/chapter_divide_and_conquer/hanota_problem/index.html index 7b28c5321..7247b9c56 100644 --- a/en/chapter_divide_and_conquer/hanota_problem/index.html +++ b/en/chapter_divide_and_conquer/hanota_problem/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_divide_and_conquer/index.html b/en/chapter_divide_and_conquer/index.html index 466d61327..0b64e8b90 100644 --- a/en/chapter_divide_and_conquer/index.html +++ b/en/chapter_divide_and_conquer/index.html @@ -65,8 +65,8 @@ - - + + diff --git 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a/en/chapter_dynamic_programming/edit_distance_problem/index.html b/en/chapter_dynamic_programming/edit_distance_problem/index.html index 2cb44b29b..d69b9654d 100644 --- a/en/chapter_dynamic_programming/edit_distance_problem/index.html +++ b/en/chapter_dynamic_programming/edit_distance_problem/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_dynamic_programming/index.html b/en/chapter_dynamic_programming/index.html index ba6f82e36..28b11728d 100644 --- a/en/chapter_dynamic_programming/index.html +++ b/en/chapter_dynamic_programming/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_dynamic_programming/intro_to_dynamic_programming/index.html b/en/chapter_dynamic_programming/intro_to_dynamic_programming/index.html index 0a490a806..425c50773 100644 --- a/en/chapter_dynamic_programming/intro_to_dynamic_programming/index.html +++ b/en/chapter_dynamic_programming/intro_to_dynamic_programming/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_dynamic_programming/knapsack_problem/index.html b/en/chapter_dynamic_programming/knapsack_problem/index.html index f72189a3e..a43b1d08f 100644 --- a/en/chapter_dynamic_programming/knapsack_problem/index.html +++ b/en/chapter_dynamic_programming/knapsack_problem/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_dynamic_programming/summary/index.html b/en/chapter_dynamic_programming/summary/index.html index 4493d3f79..7d8d08d11 100644 --- a/en/chapter_dynamic_programming/summary/index.html +++ b/en/chapter_dynamic_programming/summary/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_dynamic_programming/unbounded_knapsack_problem/index.html b/en/chapter_dynamic_programming/unbounded_knapsack_problem/index.html index a87a978ca..83ba0736b 100644 --- a/en/chapter_dynamic_programming/unbounded_knapsack_problem/index.html +++ b/en/chapter_dynamic_programming/unbounded_knapsack_problem/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_graph/graph/index.html b/en/chapter_graph/graph/index.html index 9dbc74e7c..cc9782976 100644 --- a/en/chapter_graph/graph/index.html +++ b/en/chapter_graph/graph/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_graph/graph_operations/index.html b/en/chapter_graph/graph_operations/index.html index db7431ea9..c63004c18 100644 --- a/en/chapter_graph/graph_operations/index.html +++ b/en/chapter_graph/graph_operations/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_graph/graph_traversal/index.html b/en/chapter_graph/graph_traversal/index.html index f332ce950..a61480884 100644 --- a/en/chapter_graph/graph_traversal/index.html +++ b/en/chapter_graph/graph_traversal/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_graph/index.html b/en/chapter_graph/index.html index 54772a216..993221d70 100644 --- a/en/chapter_graph/index.html +++ b/en/chapter_graph/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_graph/summary/index.html b/en/chapter_graph/summary/index.html index fe269f6e7..7f497da2d 100644 --- a/en/chapter_graph/summary/index.html +++ b/en/chapter_graph/summary/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_greedy/fractional_knapsack_problem/index.html b/en/chapter_greedy/fractional_knapsack_problem/index.html index caf7e47bd..95f75a114 100644 --- a/en/chapter_greedy/fractional_knapsack_problem/index.html +++ b/en/chapter_greedy/fractional_knapsack_problem/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_greedy/greedy_algorithm/index.html b/en/chapter_greedy/greedy_algorithm/index.html index 3a9dbb2cd..0a19e1d8e 100644 --- a/en/chapter_greedy/greedy_algorithm/index.html +++ b/en/chapter_greedy/greedy_algorithm/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_greedy/index.html b/en/chapter_greedy/index.html index 9f6d79b0f..eaca12393 100644 --- a/en/chapter_greedy/index.html +++ b/en/chapter_greedy/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_greedy/max_capacity_problem/index.html b/en/chapter_greedy/max_capacity_problem/index.html index a77222f60..e208343c7 100644 --- a/en/chapter_greedy/max_capacity_problem/index.html +++ b/en/chapter_greedy/max_capacity_problem/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_greedy/max_product_cutting_problem/index.html b/en/chapter_greedy/max_product_cutting_problem/index.html index 2cb704b38..d6153eff2 100644 --- a/en/chapter_greedy/max_product_cutting_problem/index.html +++ b/en/chapter_greedy/max_product_cutting_problem/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_greedy/summary/index.html b/en/chapter_greedy/summary/index.html index 6ea60aa60..b9263c45e 100644 --- a/en/chapter_greedy/summary/index.html +++ b/en/chapter_greedy/summary/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_hashing/hash_algorithm/index.html b/en/chapter_hashing/hash_algorithm/index.html index 717099b94..c557ca2a3 100644 --- a/en/chapter_hashing/hash_algorithm/index.html +++ b/en/chapter_hashing/hash_algorithm/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_hashing/hash_collision/index.html b/en/chapter_hashing/hash_collision/index.html index fbc521944..702d28dd4 100644 --- a/en/chapter_hashing/hash_collision/index.html +++ b/en/chapter_hashing/hash_collision/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_hashing/hash_map/index.html b/en/chapter_hashing/hash_map/index.html index 3e57668a2..d08793a45 100644 --- a/en/chapter_hashing/hash_map/index.html +++ b/en/chapter_hashing/hash_map/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_hashing/index.html b/en/chapter_hashing/index.html index 0448da6aa..d0e0718fe 100644 --- a/en/chapter_hashing/index.html +++ b/en/chapter_hashing/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_hashing/summary/index.html b/en/chapter_hashing/summary/index.html index 944a35e49..7d8e64bd4 100644 --- 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a/en/chapter_heap/top_k/index.html b/en/chapter_heap/top_k/index.html index 2ca87bfb3..34aefe7c1 100644 --- a/en/chapter_heap/top_k/index.html +++ b/en/chapter_heap/top_k/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_hello_algo/index.html b/en/chapter_hello_algo/index.html index 7b56fa3b7..347d3e59c 100644 --- a/en/chapter_hello_algo/index.html +++ b/en/chapter_hello_algo/index.html @@ -63,8 +63,8 @@ - - + + diff --git a/en/chapter_introduction/algorithms_are_everywhere/index.html b/en/chapter_introduction/algorithms_are_everywhere/index.html index b990cb4d5..ea87c7cc1 100644 --- a/en/chapter_introduction/algorithms_are_everywhere/index.html +++ b/en/chapter_introduction/algorithms_are_everywhere/index.html @@ -65,8 +65,8 @@ - - + + diff --git a/en/chapter_introduction/index.html b/en/chapter_introduction/index.html index 764412f97..09c437c5c 100644 --- a/en/chapter_introduction/index.html +++ b/en/chapter_introduction/index.html @@ -65,8 +65,8 @@ - - + + diff --git 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紙の書籍

+

長い時間をかけて磨き上げた『Hello アルゴリズム』の紙の書籍が、ついに発売されました！今の気持ちは、次の一節で表せます：

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風を追い月を追って立ち止まるな、草原の果てには春の山がある。

+ +

+

以下の動画では紙の書籍を紹介しており、私の考えもいくつか含まれています：

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    +
  • データ構造とアルゴリズムを学ぶ重要性。
    • +
  • なぜ紙の書籍で Python を選んだのか。
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  • 知識共有に対する理解。
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+
+

新人 UP 主ですので、ぜひ応援と高評価・チャンネル登録をお願いします～ありがとうございます！

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+ +
+ +

紙の書籍のスナップショット：

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+

+

長所と短所

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紙の書籍ならではの魅力を、簡単にまとめると次のとおりです：

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    +
  • フルカラー印刷を採用し、本書の「アニメーション図解」の強みをそのまま活かせます。
    • +
  • 紙の素材にもこだわり、色彩を高い精度で再現しつつ、紙の書籍ならではの質感も残しています。
    • +
  • 紙の書籍版は Web 版よりも書式が整っており、たとえば図中の数式には斜体を用いています。
    • +
  • 価格を上げずに、マインドマップの折り込みページやしおりも付属します。
    • +
  • 紙の書籍、Web 版、PDF 版で内容は同期しており、自由に切り替えて読めます。
    • +
+
+

Tip

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紙の書籍と Web 版を同期させるのは難しいため、細かな違いが生じる場合があります。ご了承ください！

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+

もちろん、購入前に検討しておくべき点もいくつかあります：

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    +
  • Python 言語を使用しているため、あなたの主言語と合わない可能性があります（Python は疑似コードと捉え、考え方の理解を重視してください）。
    • +
  • フルカラー印刷は図解やコードの読みやすさを大きく高める一方で、白黒印刷より価格はやや高くなります。
    • +
+
+

Tip

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「印刷品質」と「価格」は、アルゴリズムにおける「時間効率」と「空間効率」のようなもので、両立は容易ではありません。そして私は、「印刷品質」は「時間効率」に当たるため、より重視すべきだと考えています。

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+

購入リンク

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紙の書籍に興味があれば、ぜひ一冊ご検討ください。新刊の 5 割引を用意していただきましたので、こちらのリンクをご覧いただくか、以下の QR コードをスキャンしてください：

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+

あとがき

+

当初、私は紙の書籍出版に必要な作業量を甘く見ていて、オープンソースプロジェクトをきちんと保守していれば、紙の書籍版も何らかの自動化手段で生成できると思っていました。実際には、紙の書籍の制作フローとオープンソースプロジェクトの更新の仕組みには大きな違いがあり、その間をつなぐには多くの追加作業が必要でした。

+

一冊の本の初稿と出版基準を満たす完成稿との間には、なお大きな隔たりがあります。出版社（企画、編集、デザイン、マーケティングなど）と著者が力を合わせ、長い時間をかけて磨き上げていく必要があります。ここで、図霊の企画編集者である王軍花さん、そして人民郵電出版社と図霊コミュニティで本書の出版工程に携わってくださったすべての皆さまに感謝いたします！

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この本があなたの助けになれば幸いです！

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ご意見、ご質問、ご提案があればぜひコメントしてください
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+ Copyright © 2026 krahets
The website content is licensed under CC BY-NC-SA 4.0 +
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+ + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/ja/chapter_preface/about_the_book/index.html b/ja/chapter_preface/about_the_book/index.html index a92e17f70..57497669f 100644 --- a/ja/chapter_preface/about_the_book/index.html +++ b/ja/chapter_preface/about_the_book/index.html @@ -6,7 +6,7 @@ - + @@ -39,7 +39,7 @@ - 0.1 この本について - Hello アルゴリズム + 0.1 本書について - Hello アルゴリズム @@ -117,7 +117,7 @@ - 日本語版審閱者を募集しています！詳細は CONTRIBUTING.md を参照してください。 + 日本語版のレビュアーを募集しています。詳しくは こちら をご覧ください。 @@ -152,7 +152,7 @@
- 0.1   この本について + 0.1   本書について
@@ -341,7 +341,7 @@ - 序 + はじめに @@ -358,7 +358,7 @@ - 序 + はじめに @@ -701,7 +701,7 @@ - 1.1   アルゴリズムはどこにでもある + 1.1   アルゴリズムは至るところにある @@ -729,7 +729,7 @@ - 1.2   アルゴリズムとは何か + 1.2   アルゴリズムとは @@ -866,7 +866,7 @@ - 2.1   アルゴリズムの効率評価 + 2.1   アルゴリズム効率の評価 @@ -1143,7 +1143,7 @@ - 3.3   数値の符号化 * + 3.3   数値エンコーディング * @@ -1171,7 +1171,7 @@ - 3.4   文字の符号化 * + 3.4   文字エンコーディング * @@ -1674,7 +1674,7 @@ - 第 6 章   ハッシュ表 + 第 6 章   ハッシュテーブル @@ -1696,7 +1696,7 @@ - 第 6 章   ハッシュ表 + 第 6 章   ハッシュテーブル @@ -1718,7 +1718,7 @@ - 6.1   ハッシュ表 + 6.1   ハッシュテーブル @@ -2025,7 +2025,7 @@ - 7.5   AVL木 * + 7.5   AVL 木 * @@ -2188,7 +2188,7 @@ - 8.2   ヒープ構築操作 + 8.2   ヒープ構築 @@ -2574,7 +2574,7 @@ - 10.2   二分探索の挿入点 + 10.2   二分探索の挿入位置 @@ -2630,7 +2630,7 @@ - 10.4   ハッシュ最適化戦略 + 10.4   ハッシュによる最適化戦略 @@ -2658,7 +2658,7 @@ - 10.5   探索アルゴリズムの再認識 + 10.5   探索アルゴリズム再考 @@ -3196,7 +3196,7 @@ - 12.1   分割統治アルゴリズム + 12.1   分割統治法 @@ -3252,7 +3252,7 @@ - 12.3   木の構築問題 + 12.3   二分木の構築問題 @@ -3280,7 +3280,7 @@ - 12.4   ハノイの塔問題 + 12.4   ハノイの塔の問題 @@ -3473,7 +3473,7 @@ - 13.3   部分集合和問題 + 13.3   部分和問題 @@ -3501,7 +3501,7 @@ - 13.4   Nクイーン問題 + 13.4   n クイーン問題 @@ -3642,7 +3642,7 @@ - 14.1   動的計画法の初歩 + 14.1   動的計画法入門 @@ -3670,7 +3670,7 @@ - 14.2   DP 問題の特性 + 14.2   動的計画法の問題特性 @@ -3698,7 +3698,7 @@ - 14.3   DP の解法の考え方 + 14.3   動的計画法の問題解決の考え方 @@ -3726,7 +3726,7 @@ - 14.4   0-1ナップサック問題 + 14.4   0-1 ナップサック問題 @@ -3919,7 +3919,7 @@ - 15.1   貪欲アルゴリズム + 15.1   貪欲法 @@ -4164,7 +4164,7 @@ - 16.2   一緒に創作に参加する + 16.2   一緒に制作に参加しましょう @@ -4376,47 +4376,48 @@ -

0.1   この本について

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このオープンソースプロジェクトは、データ構造とアルゴリズムに関する無料で初心者にやさしいクラッシュコースの作成を目指しています。

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0.1   本書について

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本プロジェクトは、オープンソースで無料、かつ初心者にやさしいデータ構造とアルゴリズムの入門書を作ることを目的としています。

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  • アニメーション付きの図解、理解しやすい内容、滑らかな学習曲線により、初心者がデータ構造とアルゴリズムの「知識マップ」を探索するのに役立ちます。
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  • ワンクリックでコードを実行できるため、読者のプログラミングスキルの向上と、アルゴリズムの動作原理およびデータ構造の基礎実装の理解に役立ちます。
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  • 教えることによる学習を促進し、質問や洞察の共有を自由に行ってください。議論を通じて一緒に成長しましょう。
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  • 全編でアニメーション付きの図解を採用し、内容は明快で理解しやすく、学習曲線もなだらかで、初心者がデータ構造とアルゴリズムの知識地図を探求できるよう導きます。
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  • ソースコードはワンクリックで実行でき、読者が演習を通じてプログラミング能力を高め、アルゴリズムの動作原理とデータ構造の内部実装を理解する助けとなります。
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  • 読者どうしの助け合いによる学習を推奨しており、コメント欄で質問や見解を共有し、対話と議論を通じてともに成長していくことを歓迎します。

0.1.1   対象読者

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もしあなたがアルゴリズムに触れたばかりで経験が限られている場合、またはアルゴリズムである程度の経験を積んでいても、データ構造とアルゴリズムについて曖昧な理解しかなく、常に「分かった」と「うーん」の間を行き来している場合、この本はあなたのためのものです！

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すでにある程度の問題解決経験を積んでおり、ほとんどのタイプの問題に精通している場合、この本はアルゴリズムの知識体系を復習し整理するのに役立ちます。リポジトリのソースコードは「問題解決ツールキット」や「アルゴリズムチートシート」として使用できます。

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もしあなたがアルゴリズムの専門家であれば、貴重な提案をいただくか、参加して協力していただければと思います。

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もしあなたがアルゴリズム初心者で、これまでアルゴリズムに触れたことがない、あるいはすでに多少の問題演習の経験はあるものの、データ構造とアルゴリズムについてはまだ曖昧な理解にとどまり、できるかできないかの間を行き来しているなら、本書はまさにあなたのために作られています！

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もしすでに一定量の問題演習を積み、ほとんどの問題パターンに慣れているなら、本書はアルゴリズム知識体系の復習と整理に役立ちます。リポジトリのソースコードは「問題演習ツール集」や「アルゴリズム辞典」として活用できます。

+

もしあなたがアルゴリズムの「達人」なら、貴重なご提案をいただけることを楽しみにしています。あるいは一緒に執筆に参加してください。

前提条件

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少なくとも一つのプログラミング言語で簡単なコードを書いて読むことができる必要があります。

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少なくともいずれか一つの言語でのプログラミング基礎があり、簡単なコードを読んだり書いたりできる必要があります。

0.1.2   内容構成

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本書の主な内容を下図に示します。

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本書の主な内容は以下の図のとおりです。

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  • 計算量解析: データ構造とアルゴリズムを評価する側面と方法を探求します。時間計算量と空間計算量を導出する方法、および一般的なタイプと例を扱います。
    • -
  • データ構造: 基本的なデータ型、分類方法、定義、長所と短所、一般的な操作、タイプ、応用、および配列、連結リスト、スタック、キュー、ハッシュテーブル、木、ヒープ、グラフなどのデータ構造の実装方法に焦点を当てます。
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  • アルゴリズム: アルゴリズムを定義し、その長所と短所、効率性、応用シナリオ、問題解決ステップについて議論し、検索、ソート、分割統治、バックトラッキング、動的プログラミング、貪欲アルゴリズムなど、さまざまなアルゴリズムのサンプル問題を含みます。
    • +
  • 計算量解析：データ構造とアルゴリズムを評価する観点と方法。時間計算量と空間計算量の求め方、代表的な種類、例など。
    • +
  • データ構造：基本データ型とデータ構造の分類方法。配列、連結リスト、スタック、キュー、ハッシュテーブル、木、ヒープ、グラフなどのデータ構造の定義、長所と短所、基本操作、代表的な種類、典型的な応用、実装方法など。
    • +
  • アルゴリズム：探索、ソート、分割統治、バックトラッキング、動的計画法、貪欲法などのアルゴリズムの定義、長所と短所、効率、適用場面、問題を解く手順、例題など。

本書の主な内容

図 0-1   本書の主な内容

0.1.3   謝辞

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本書は、オープンソースコミュニティの多数の貢献者による共同の努力のもと、継続的に改善されています。時間と労力を注いで執筆に携わってくださったすべての方々に感謝します。貢献者は以下のとおりです（GitHub により自動生成された順序）：krahets、coderonion、Gonglja、nuomi1、Reanon、justin-tse、hpstory、danielsss、curtishd、night-cruise、S-N-O-R-L-A-X、rongyi、msk397、gvenusleo、khoaxuantu、rivertwilight、K3v123、gyt95、zhuoqinyue、yuelinxin、Zuoxun、mingXta、Phoenix0415、FangYuan33、GN-Yu、longsizhuo、IsChristina、xBLACKICEx、guowei-gong、Cathay-Chen、pengchzn、QiLOL、magentaqin、hello-ikun、JoseHung、qualifier1024、thomasq0、sunshinesDL、L-Super、Guanngxu、Transmigration-zhou、WSL0809、Slone123c、lhxsm、yuan0221、what-is-me、Shyam-Chen、theNefelibatas、longranger2、codeberg-user、xiongsp、JeffersonHuang、prinpal、seven1240、Wonderdch、malone6、xiaomiusa87、gaofer、bluebean-cloud、a16su、SamJin98、hongyun-robot、nanlei、XiaChuerwu、yd-j、iron-irax、mgisr、steventimes、junminhong、heshuyue、danny900714、MolDuM、Nigh、Dr-XYZ、XC-Zero、reeswell、PXG-XPG、NI-SW、Horbin-Magician、Enlightenus、YangXuanyi、beatrix-chan、DullSword、xjr7670、jiaxianhua、qq909244296、iStig、boloboloda、hts0000、gledfish、wenjianmin、keshida、kilikilikid、lclc6、lwbaptx、linyejoe2、liuxjerry、llql1211、fbigm、echo1937、szu17dmy、dshlstarr、Yucao-cy、coderlef、czruby、bongbongbakudan、beintentional、ZongYangL、ZhongYuuu、ZhongGuanbin、hezhizhen、linzeyan、ZJKung、luluxia、xb534、ztkuaikuai、yw-1021、ElaBosak233、baagod、zhouLion、yishangzhang、yi427、yanedie、yabo083、weibk、wangwang105、th1nk3r-ing、tao363、4yDX3906、syd168、sslmj2020、smilelsb、siqyka、selear、sdshaoda、Xi-Row、popozhu、nuquist19、noobcodemaker、XiaoK29、chadyi、lyl625760、lucaswangdev、0130w、shanghai-Jerry、EJackYang、Javesun99、eltociear、lipusheng、KNChiu、BlindTerran、ShiMaRing、lovelock、FreddieLi、FloranceYeh、fanchenggang、gltianwen、goerll、nedchu、curly210102、CuB3y0nd、KraHsu、CarrotDLaw、youshaoXG、bubble9um、Asashishi、Asa0oo0o0o、fanenr、eagleanurag、akshiterate、52coder、foursevenlove、KorsChen、GaochaoZhu、hopkings2008、yang-le、realwujing、Evilrabbit520、Umer-Jahangir、Turing-1024-Lee、Suremotoo、paoxiaomooo、Chieko-Seren、Allen-Scai、ymmmas、Risuntsy、Richard-Zhang1019、RafaelCaso、qingpeng9802、primexiao、Urbaner3、zhongfq、nidhoggfgg、MwumLi、CreatorMetaSky、martinx、ZnYang2018、hugtyftg、logan-qiu、psychelzh、Keynman、KeiichiKasai、KawaiiAsh。

-

この本のコードレビュー作業は、coderonion, Gonglja, gvenusleo, hpstory, justin‐tse, khoaxuantu, krahets, night-cruise, nuomi1, Reanon and rongyi（アルファベット順）によって完了されました。彼らの時間と努力に感謝し、様々な言語でのコードの標準化と統一性を確保してくださいました。

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本書の繁体字中国語版は Shyam-Chen および Dr-XYZ によってレビューされ、英語版は yuelinxin、K3v123、QiLOL、Phoenix0415、SamJin98、yanedie、RafaelCaso、pengchzn、thomasq0、magentaqin によってレビューされ、日本語版は eltociear によってレビューされました。彼らの継続的な貢献のおかげで、本書はより幅広い読者層に提供することができています。ここに深く感謝いたします。

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この本の制作過程において、多くの方々から貴重な支援をいただきました。これらに限定されませんが：

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本書は、オープンソースコミュニティの多くの貢献者による共同の努力のもとで、継続的に改善されています。時間と労力を注いでくださったすべての執筆者の皆さんに感謝します。お名前は次のとおりです（GitHub により自動生成された順序）：krahets、coderonion、Gonglja、nuomi1、Reanon、justin-tse、hpstory、danielsss、curtishd、night-cruise、S-N-O-R-L-A-X、rongyi、msk397、gvenusleo、khoaxuantu、rivertwilight、K3v123、gyt95、zhuoqinyue、yuelinxin、Zuoxun、mingXta、Phoenix0415、FangYuan33、GN-Yu、longsizhuo、IsChristina、xBLACKICEx、guowei-gong、Cathay-Chen、pengchzn、QiLOL、magentaqin、hello-ikun、JoseHung、qualifier1024、thomasq0、sunshinesDL、L-Super、Guanngxu、Transmigration-zhou、WSL0809、Slone123c、lhxsm、yuan0221、what-is-me、Shyam-Chen、theNefelibatas、longranger2、codeberg-user、xiongsp、JeffersonHuang、prinpal、seven1240、Wonderdch、malone6、xiaomiusa87、gaofer、bluebean-cloud、a16su、SamJin98、hongyun-robot、nanlei、XiaChuerwu、yd-j、iron-irax、mgisr、steventimes、junminhong、heshuyue、danny900714、MolDuM、Nigh、Dr-XYZ、XC-Zero、reeswell、PXG-XPG、NI-SW、Horbin-Magician、Enlightenus、YangXuanyi、beatrix-chan、DullSword、xjr7670、jiaxianhua、qq909244296、iStig、boloboloda、hts0000、gledfish、wenjianmin、keshida、kilikilikid、lclc6、lwbaptx、linyejoe2、liuxjerry、llql1211、fbigm、echo1937、szu17dmy、dshlstarr、Yucao-cy、coderlef、czruby、bongbongbakudan、beintentional、ZongYangL、ZhongYuuu、ZhongGuanbin、hezhizhen、linzeyan、ZJKung、luluxia、xb534、ztkuaikuai、yw-1021、ElaBosak233、baagod、zhouLion、yishangzhang、yi427、yanedie、yabo083、weibk、wangwang105、th1nk3r-ing、tao363、4yDX3906、syd168、sslmj2020、smilelsb、siqyka、selear、sdshaoda、Xi-Row、popozhu、nuquist19、noobcodemaker、XiaoK29、chadyi、lyl625760、lucaswangdev、0130w、shanghai-Jerry、EJackYang、Javesun99、eltociear、lipusheng、KNChiu、BlindTerran、ShiMaRing、lovelock、FreddieLi、FloranceYeh、fanchenggang、gltianwen、goerll、nedchu、curly210102、CuB3y0nd、KraHsu、CarrotDLaw、youshaoXG、bubble9um、Asashishi、Asa0oo0o0o、fanenr、eagleanurag、akshiterate、52coder、foursevenlove、KorsChen、GaochaoZhu、hopkings2008、yang-le、realwujing、Evilrabbit520、Umer-Jahangir、Turing-1024-Lee、Suremotoo、paoxiaomooo、Chieko-Seren、Allen-Scai、ymmmas、Risuntsy、Richard-Zhang1019、RafaelCaso、qingpeng9802、primexiao、Urbaner3、zhongfq、nidhoggfgg、MwumLi、CreatorMetaSky、martinx、ZnYang2018、hugtyftg、logan-qiu、psychelzh、Keynman、KeiichiKasai と KawaiiAsh。

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本書のコードレビューは coderonion、curtishd、Gonglja、gvenusleo、hpstory、justin-tse、khoaxuantu、krahets、night-cruise、nuomi1、Reanon と rongyi によって行われました（アルファベット順）。彼らが費やしてくれた時間と労力に感謝します。各言語のコードの規範性と統一性が保たれているのは、まさに彼らのおかげです。

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本書の繁体字中国語版は Shyam-Chen と Dr-XYZ がレビューし、英語版は yuelinxin、K3v123、QiLOL、Phoenix0415、SamJin98、yanedie、RafaelCaso、pengchzn、thomasq0 と magentaqin がレビューし、日本語版は eltociear がレビューしました。彼らの継続的な貢献があってこそ、本書はより幅広い読者に届けられています。感謝いたします。

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本書の ePub 電子書籍生成ツールは zhongfq によって開発されました。彼の貢献に感謝します。読者により自由な読書方法を提供してくれました。

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本書の執筆過程で、私は多くの方々の助けを得ました。

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  • 会社でのメンター、李熙博士に感謝します。ある会話で「早く行動しろ」と励ましていただき、この本を書く決意を固めることができました。
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  • ガールフレンドのBubbleに感謝します。この本の最初の読者として、アルゴリズム初心者の視点から多くの貴重な提案をいただき、この本を初心者により適したものにしてくださいました。
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  • Tengbao、Qibao、Feibaoに感謝します。この本のクリエイティブな名前を考えてくださり、みんなが初めて「Hello World!」を書いた時の素晴らしい思い出を呼び起こしてくれました。
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  • Xiaoquanに感謝します。知的財産に関する専門的な支援を提供してくださり、このオープンソース本の開発において重要な役割を果たしてくださいました。
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  • Sutongに感謝します。この本の美しいカバーとロゴをデザインしてくださり、私の要求で何度も修正を辛抱強く行ってくださいました。
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  • @squidfunk に感謝します。執筆と組版の提案、および彼が開発したオープンソースドキュメントテーマ Material-for-MkDocs を提供してくださいました。
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  • 会社での私の指導教員である李汐博士に感謝します。ある対話の中で「すぐに行動しよう」と励ましてくださり、この本を書く決意を固めることができました；
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  • 私の恋人であり、本書の最初の読者でもある泡泡に感謝します。アルゴリズム初心者の視点から多くの貴重な提案をしてくれたおかげで、本書はより初心者に適したものになりました；
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  • 腾宝、琦宝、飞宝が本書に創造性あふれる名前を付けてくれたことに感謝します。みんなが最初のコード行「Hello World!」を書いた美しい記憶を呼び起こしてくれました；
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  • 校铨が知的財産の面で専門的な支援をしてくれたことに感謝します。これは本オープンソース書籍の改善に重要な役割を果たしました；
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  • 苏潼が本書の美しい表紙と logo をデザインし、私の完璧主義につき合って何度も辛抱強く修正してくれたことに感謝します；
    • +
  • @squidfunk が組版に関する助言を提供してくれたこと、そして彼が開発したオープンソースのドキュメントテーマ Material-for-MkDocs に感謝します。
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執筆の過程で、データ構造とアルゴリズムに関する多数の教科書や記事を深く研究しました。これらの作品は模範的なモデルとして機能し、この本の内容の正確性と品質を確保してくださいました。先人の方々の貴重な貢献に感謝いたします！

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この本は、理論と実践を組み合わせた学習を提唱しており、この点で "Dive into Deep Learning" からインスピレーションを受けています。この優れた本をすべての読者に強くお勧めします。

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継続的な支援と励ましにより、この興味深い仕事をすることを可能にしてくださった両親に心から感謝いたします。

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執筆の過程で、私はデータ構造とアルゴリズムに関する多くの教材や記事を読みました。これらの作品は本書に優れた手本を与え、本書の内容の正確性と品質を支えてくれました。ここに、すべての先生方と先人たちの卓越した貢献に感謝します！

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本書は手と頭を同時に使う学習方法を提唱しています。この点で私は『手を動かして学ぶ深層学習』から大きな啓発を受けました。ここで読者の皆さんにこの優れた著作を強くお勧めします。

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心から両親に感謝します。いつも支え励ましてくれたからこそ、私はこの興味深いことに取り組む機会を得ることができました。

@@ -4439,7 +4440,7 @@ aria-label="フッター" diff --git a/ja/chapter_preface/index.html b/ja/chapter_preface/index.html index 75e47b475..f7941a88b 100644 --- a/ja/chapter_preface/index.html +++ b/ja/chapter_preface/index.html @@ -6,7 +6,7 @@ - + @@ -39,7 +39,7 @@ - 第 0 章 序文 - Hello アルゴリズム + 第 0 章 はじめに - Hello アルゴリズム @@ -117,7 +117,7 @@ - 日本語版審閱者を募集しています！詳細は CONTRIBUTING.md を参照してください。 + 日本語版のレビュアーを募集しています。詳しくは こちら をご覧ください。 @@ -152,7 +152,7 @@
- 第 0 章   序文 + 第 0 章   はじめに
@@ -341,7 +341,7 @@ - 序 + はじめに @@ -358,7 +358,7 @@ - 序 + はじめに @@ -620,7 +620,7 @@ - 1.1   アルゴリズムはどこにでもある + 1.1   アルゴリズムは至るところにある @@ -648,7 +648,7 @@ - 1.2   アルゴリズムとは何か + 1.2   アルゴリズムとは @@ -785,7 +785,7 @@ - 2.1   アルゴリズムの効率評価 + 2.1   アルゴリズム効率の評価 @@ -1062,7 +1062,7 @@ - 3.3   数値の符号化 * + 3.3   数値エンコーディング * @@ -1090,7 +1090,7 @@ - 3.4   文字の符号化 * + 3.4   文字エンコーディング * @@ -1593,7 +1593,7 @@ - 第 6 章   ハッシュ表 + 第 6 章   ハッシュテーブル @@ -1615,7 +1615,7 @@ - 第 6 章   ハッシュ表 + 第 6 章   ハッシュテーブル @@ -1637,7 +1637,7 @@ - 6.1   ハッシュ表 + 6.1   ハッシュテーブル @@ -1944,7 +1944,7 @@ - 7.5   AVL木 * + 7.5   AVL 木 * @@ -2107,7 +2107,7 @@ - 8.2   ヒープ構築操作 + 8.2   ヒープ構築 @@ -2493,7 +2493,7 @@ - 10.2   二分探索の挿入点 + 10.2   二分探索の挿入位置 @@ -2549,7 +2549,7 @@ - 10.4   ハッシュ最適化戦略 + 10.4   ハッシュによる最適化戦略 @@ -2577,7 +2577,7 @@ - 10.5   探索アルゴリズムの再認識 + 10.5   探索アルゴリズム再考 @@ -3115,7 +3115,7 @@ - 12.1   分割統治アルゴリズム + 12.1   分割統治法 @@ -3171,7 +3171,7 @@ - 12.3   木の構築問題 + 12.3   二分木の構築問題 @@ -3199,7 +3199,7 @@ - 12.4   ハノイの塔問題 + 12.4   ハノイの塔の問題 @@ -3392,7 +3392,7 @@ - 13.3   部分集合和問題 + 13.3   部分和問題 @@ -3420,7 +3420,7 @@ - 13.4   Nクイーン問題 + 13.4   n クイーン問題 @@ -3561,7 +3561,7 @@ - 14.1   動的計画法の初歩 + 14.1   動的計画法入門 @@ -3589,7 +3589,7 @@ - 14.2   DP 問題の特性 + 14.2   動的計画法の問題特性 @@ -3617,7 +3617,7 @@ - 14.3   DP の解法の考え方 + 14.3   動的計画法の問題解決の考え方 @@ -3645,7 +3645,7 @@ - 14.4   0-1ナップサック問題 + 14.4   0-1 ナップサック問題 @@ -3838,7 +3838,7 @@ - 15.1   貪欲アルゴリズム + 15.1   貪欲法 @@ -4083,7 +4083,7 @@ - 16.2   一緒に創作に参加する + 16.2   一緒に制作に参加しましょう @@ -4273,12 +4273,12 @@ -

第 0 章   序文

-

序文

+

第 0 章   はじめに

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はじめに

Abstract

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アルゴリズムは美しい交響曲のようで、コードの一行一行がリズムのように流れています。

-

この本があなたの心の中で静かに響き、独特で深い旋律を残すことを願っています。

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アルゴリズムは美しい交響曲のようであり、コードの一行一行が旋律のように流れていきます。

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この本があなたの心の中でそっと響き、独自で深い旋律を残してくれることを願っています。

章の内容

7.2.2   Прямой, симметричный и обратный обходы

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Соответственно, прямой, симметричный и обратный обходы относятся к обходу в глубину (depth-first traversal), также называемому поиском в глубину (depth-first search, DFS); он отражает идею "сначала идти до конца, затем откатываться и продолжать".

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На рисунке 7-10 показан принцип работы обхода двоичного дерева в глубину. Обход в глубину похож на то, как будто мы обходим всю двоичную структуру по внешнему контуру , и у каждого узла встречаем три позиции, соответствующие прямому, симметричному и обратному обходам.

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Соответственно, прямой, симметричный и обратный обходы относятся к обходу в глубину (depth-first traversal), также называемому поиском в глубину (depth-first search, DFS); он отражает идею "сначала идти до конца, затем возвращаться и продолжать".

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На рисунке 7-10 показан принцип работы обхода двоичного дерева в глубину. Обход в глубину можно представить как обход всей двоичной структуры по внешнему контуру , и у каждого узла встречаются три позиции, соответствующие прямому, симметричному и обратному обходам.

Прямой, симметричный и обратный обходы двоичного дерева поиска

Рисунок 7-10   Прямой, симметричный и обратный обходы двоичного дерева поиска

@@ -5328,7 +5328,7 @@ aria-label="Нижний колонтитул"

diff --git a/ru/chapter_tree/summary/index.html b/ru/chapter_tree/summary/index.html index 07bdf7f5e..6529f74ea 100644 --- a/ru/chapter_tree/summary/index.html +++ b/ru/chapter_tree/summary/index.html @@ -65,8 +65,8 @@ - - + + @@ -574,7 +574,7 @@ - Глава 1. Знакомство с алгоритмами + Глава 1. Введение в алгоритмы @@ -596,7 +596,7 @@ - Глава 1. Знакомство с алгоритмами + Глава 1. Введение в алгоритмы @@ -646,7 +646,7 @@ - 1.2 Что такое структуры данных и алгоритмы + 1.2 Что такое алгоритм @@ -1181,7 +1181,7 @@ - Глава 4. Массив и связный список + Глава 4. Массивы и списки @@ -1203,7 +1203,7 @@ - Глава 4. Массив и связный список + Глава 4. Массивы и списки @@ -1309,7 +1309,7 @@ - 4.4 Память и кеш * + 4.4 Оперативная память и кэш * @@ -1591,7 +1591,7 @@ - Глава 6. Хеширование + Глава 6. Хеш-таблицы @@ -1613,7 +1613,7 @@ - Глава 6. Хеширование + Глава 6. Хеш-таблицы @@ -1691,7 +1691,7 @@ - 6.3 Хеш-алгоритмы + 6.3 Алгоритмы хеширования @@ -1788,7 +1788,7 @@ - Глава 7. Дерево + Глава 7. Деревья @@ -1810,7 +1810,7 @@ - Глава 7. Дерево + Глава 7. Деревья @@ -1888,7 +1888,7 @@ - 7.3 Представление дерева массивом + 7.3 Представление двоичного дерева массивом @@ -1981,7 +1981,7 @@ - 7.6 Резюме + 7.6 Краткие итоги @@ -1999,7 +1999,7 @@ - 7.6 Резюме + 7.6 Краткие итоги @@ -2205,7 +2205,7 @@ - 8.3 Задача Top-K + 8.3 Задача Top-k @@ -2296,7 +2296,7 @@ - Глава 9. Граф + Глава 9. Графы @@ -2318,7 +2318,7 @@ - Глава 9. Граф + Глава 9. Графы @@ -2368,7 +2368,7 @@ - 9.2 Базовые операции над графами + 9.2 Базовые операции графа @@ -2424,7 +2424,7 @@ - 9.4 Резюме + 9.4 Краткие итоги @@ -2563,7 +2563,7 @@ - 10.2 Точка вставки двоичного поиска + 10.2 Двоичный поиск точки вставки @@ -2591,7 +2591,7 @@ - 10.3 Граничные случаи двоичного поиска + 10.3 Двоичный поиск границ @@ -2619,7 +2619,7 @@ - 10.4 Стратегия оптимизации через хеширование + 10.4 Стратегии оптимизации хеширования @@ -2647,7 +2647,7 @@ - 10.5 Алгоритмы поиска: новый взгляд + 10.5 Переосмысление алгоритмов поиска @@ -2852,7 +2852,7 @@ - 11.3 Пузырьковая сортировка + 11.3 Сортировка пузырьком @@ -2880,7 +2880,7 @@ - 11.4 Сортировка вставкой + 11.4 Сортировка вставками @@ -3185,7 +3185,7 @@ - 12.1 Алгоритмы разделяй и властвуй + 12.1 Стратегия разделяй и властвуй @@ -3213,7 +3213,7 @@ - 12.2 Стратегия поиска разделяй и властвуй + 12.2 Поисковая стратегия разделяй и властвуй @@ -3490,7 +3490,7 @@ - 13.4 Задача о $n$ ферзях + 13.4 Задача о n ферзях @@ -3631,7 +3631,7 @@ - 14.1 Введение в динамическое программирование + 14.1 Первое знакомство с динамическим программированием @@ -3743,7 +3743,7 @@ - 14.5 Задача о неограниченном рюкзаке + 14.5 Задача о полном рюкзаке @@ -4357,14 +4357,14 @@

7.6   Краткие итоги

1.   Основные моменты

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  • Двоичное дерево - это нелинейная структура данных, отражающая логику "разделения надвое". Каждый узел двоичного дерева содержит значение и два указателя, которые соответственно ведут к левому и правому дочерним узлам.
    • +
  • Двоичное дерево - это нелинейная структура данных, отражающая логику "разделяй и властвуй". Каждый узел двоичного дерева содержит значение и два указателя, которые соответственно ведут к левому и правому дочерним узлам.
  • Для любого узла двоичного дерева дерево, образованное его левым (правым) дочерним узлом и всеми нижележащими узлами, называется левым (правым) поддеревом этого узла.
  • К связанным с двоичным деревом терминам относятся корневой узел, листовой узел, уровень, степень, ребро, высота, глубина и так далее.
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  • Инициализация двоичного дерева, вставка узлов и удаление узлов похожи по способу реализации на операции со связным списком.
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  • Инициализация двоичного дерева, вставка узлов и удаление узлов аналогичны операциям со связным списком.
  • К распространенным видам двоичного дерева относятся идеальное двоичное дерево, полное двоичное дерево, строгое двоичное дерево и сбалансированное двоичное дерево. Идеальное двоичное дерево - наиболее желательное состояние, а связный список - худший случай после вырождения.
    • -
  • Двоичное дерево можно представить массивом: значения узлов и пустые позиции располагаются в порядке обхода по уровням, а связи между родителем и детьми реализуются через отображение индексов.
    • -
  • Обход двоичного дерева по уровням является методом поиска в ширину; он отражает идею "расширяться слой за слоем наружу" и обычно реализуется через очередь.
    • -
  • Прямой, симметричный и обратный обходы относятся к поиску в глубину; они отражают идею "сначала дойти до конца, затем откатиться и продолжить" и обычно реализуются рекурсивно.
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  • Двоичное дерево можно представить массивом: значения узлов и пустые позиции располагаются в порядке обхода по уровням, а связи между родителем и детьми реализуются через индексацию.
    • +
  • Обход двоичного дерева по уровням является методом поиска в ширину; он отражает идею "расширяться от центра к периферии слой за слоем" и обычно реализуется через очередь.
    • +
  • Прямой, симметричный и обратный обходы относятся к поиску в глубину; они отражают идею "сначала дойти до конца, затем вернуться и продолжить" и обычно реализуются рекурсивно.
  • Двоичное дерево поиска - это эффективная структура данных для поиска элементов; его поиск, вставка и удаление имеют временную сложность \(O(\log n)\) . Когда двоичное дерево поиска вырождается в связный список, все эти сложности деградируют до \(O(n)\) .
  • AVL-дерево, также называемое сбалансированным двоичным деревом поиска, с помощью вращений гарантирует, что после постоянных вставок и удалений узлов дерево остается сбалансированным.
  • Вращения AVL-дерева включают правое вращение, левое вращение, сначала правое затем левое и сначала левое затем правое. После вставки или удаления узла AVL-дерево выполняет вращения снизу вверх, чтобы снова восстановить баланс.
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